Question

The volume of a cone of height 5 and radius r is V=5/3πr^2. What is the radius of such a cone whose volume is 2π? r= ______

Answer 1

The volume of a cone with height h=5 is given by,

`V=(5)/(3)\pi r^2`

The volume of the above type of cone is given to be V=2π.

So, substitute V=2π in above equation and solve for r.

`\begin{gathered} 2\pi=(5)/(3)\pi r^2 \\ (2\cdot3)/(5)=r^2 \\ (6)/(5)=r^2 \\ r=\sqrt[]{(6)/(5)} \\ r=1.095 \end{gathered}`

Therefore, the radius of the cone is 1.095.